The context of the writer. Apologies if I implied that the notation semantics were important -- letter exchange is free; concept change is not. What I indented

The context of the writer. Apologies if I implied that the notation semantics were important -- letter exchange is free; concept change is not. What I indented to mean was the use of the terms poles and zeros is a bit wonky. Attempting to be cute with a physicist's hat, a pole is a "black hole", an entity you must not cross because the calculus will not work. It is a discontinuity, a singular value. There are worse things in mathematical generalizations; a cut / line in a manifold. But tools to cope.